Global Coverage By Banked Aeroglide Atmospheric Entry

The Space Congress® Proceedings
1966 (3rd) The Challenge of Space
Mar 7th, 8:00 AM
Global Coverage By Banked Aeroglide
Atmospheric Entry
Paul D. Arthur
Professor of Engineering, University of Florida, GENESYS
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Paul D. Arthur, "Global Coverage By Banked Aeroglide Atmospheric Entry" (March 7, 1966). The Space Congress® Proceedings. Paper 3.
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GLOBAL COVERAGE BY BANKED AEROGLIDE ATMOSPHERIC ENTRY
Paul D. Arthur
Professor of Engineering
Universitv of Florida
GENESYS, Port Canaveral
Summary
"Global Coverage" is defined as the capa­
bility of an atmospheric entry vehicle to
return to any point on the globe follow­
ing descent from any orbit.
Global
Coverage is not possible with current aero­
space vehicle systems, but advanced lift­
ing systems offer this promise.
Spherical earth analytical results are
presented showing a possible bank-speed
schedule (the minor circle turn) and the
necessary lift-drag ratio for Global
Coverage as a function of initial atmo­
spheric entry speed and other relevant
parameters.
Global Coverage is available
for entry at circular speed for L/D > 3.56;
for -entry at parabolic entry speed for
L/D > 2.34.
Comparision with optimized
bank programs give indication that this
minor circle maneuver is close to "optimum"
and will provide a practical guidance
scheme for controlled atmospheric entry
from space.
No tat ion
D
g
h
L
L/D
m
Q
r
V
Vc
3
Y
<j>
ty
X
n
Aerodynamic drag force
Proportionality factor between weight
and mass
Altitude of entry vehicle above planet
surface
Aerodynamic lift force
Aerodynamic lift-drag ratio
Entry vehicle mass
Minor circle turn parameter-constant
during the maneuver
Radius to center of planet
Speed
Circular orbit speed, /gr
- 26,000
feet per second at the Earth
Bank angle of entry vehicle-measured
from wings level condition
Flight path angle - measured up from
horizon
Latitude angle - measured from the
plane of the equator
Heading angle - measured north from
due east
Longitude angle - measured east from
initial point of maneuver
The square of the speed ratio, V 2 /gr
Lateral Maneuver Techniques
Lateral maneuver capability will be requir­
ed in the return from space of advanced
entry vehicles.
The down range landing
point can be adjusted by the orbit deboost
location and deboost velocity but cross
range can only be provided by extra atmo­
spheric thrust, propulsion during entry
(aerocruise) , or atmospheric glide (aeroglide) .
Cross range capability will permit consid­
erable operational flexibility, such as re­
turn to more landing sites or quicker return
to a specified site .
Horizontal landing
will be possible with the higher L/D values
discussed here: thus touch-downs can be
handled routinely, as opposed to the extra­
ordinary task force required for present
Mercury/Gemini type returns which have very
little lateral capability.
Extra atmospheric propulsion (a rocket im­
pulse before entering the atmosphere) is
one way to provide lateral capability.
Simple orbit plane rotation requires about
450 fps per degree, or 7 fps per nautical
mile lateral displacement one quarter rev­
olution later.
Yawing the deboost retrofire
impulse reduces this cost for small excur­
sions of lateral range.
But large lateral
capability of several thousand miles re­
quires prohibitive velocity impulse values;
for example over 26,000 fps to land at the
pole from an orbit initially in the plane
of the equator.
The promising concepts of propulsion during
entry (aerocruise and other techniques) have
been presented previously. 1 ^ 3
Further work
in this direction is currently under USAF
contract and will be reported later.
Fey 4
has studied the use of aerodynamic maneuvers
during boost propulsion to attain an orbit
plane which does not contain the launch site.
Minor Circle Aeroglide Solutions
In contrast, the present paper will discuss
lateral maneuvering by aerodynamic atmo^
spheric entry.
The aeroglide concept has been studied for
some years.
Early numerical and analytical
studies utilized truncated equations of
motion (for example, Slye 5 ) which can be
identified as appropriate for a "cylindrical
planet" model.
Generally, these truncated
equations gave lateral glide ranges which
were too large.
Jackson 6 identified this
difficulty and suggested an analytical so­
lution which is just a minor circle on the
planet surface. 7 *^ The equations of motion
for a shallow glide in vertical equilibrum
are given below.
The terms underlined are
those discarded for the truncated "cylindri­
cal planet" solution.
If the centrifugal
force term (mgn) of equation (1) is further
abandoned, the model is of a "flat planet".
Lcos3 = mg (1-n) where r|A. V 2
LsinS =
D + mV = 0
629
+ mVAp sine})
(D
(2)
(3)
These three equations give the orthogonal
force balances: the kinematics provide:
VX
(A)
r d) = Vs ini/;
o
\ =
(6)
r ,cos d>
The "Cylindrical Planet" Solution
Application of the same constant Q bankspeed program to the truncated (cylindrical)
equations (equations 1-6, neglecting under­
lined terms) yields a plane circle in the
longitude-latitude
(5)
For a particular bank schedule with
speed, an analytical solution of the
full spherical set of equations wa.s
recognized as a minor circle on the
planet, tangent to the original entry
plane.
For east entry in the equato­
rial plane, the minor circle longitudelatitude trace is given by
(8)
These expressions are considerable simpli­
fications of equations 12 and 20 of refer­
ence 8. The requisite bank schedule is a
simple function of speed and the minor
circle parameter Q, given by the expres­
sion
tanB = Qn_
l-n
(10)
sinij; = QX
(11)
This provides the only known analytical so­
lution for direct comparison of the spherical
and cylindrical sets of equations.
These
spherical and cylindrical solutions are sketch­
ed in figure two, for glides from circular
speed at Q = 1 , verifying and systematizing
the previous numerical results.
Note that
the spherical and cylindrical latitudes for
Q = 1 are nearly coincident functions of L/D,
although the trajectories are entirely differ­
ent.
Thus latitude data alone may not be suf­
ficient to evaluate the accuracy of a set of
truncated entry equations.
Qcoscf)
The heading angle is available as
= QsinX
X2 =
Global Coverage Lift Drag Ratio
The minor circle turn bank schedule is supe­
rior to constant bank schedules
for genera­
tion of lateral range, as large bank angle
is used at near circular speed to generate
initial heading change.
While the bank sched­
ule as a function of speed maintains the ve­
hicle on the minor circle, it is the energy
balance which specifies the trajectory length
alon g the minor circle.
Both high aerodynamic
lift drag ratio (L/D) and high initial speed
propagate the glide farther along the minor
circle.
Thus it is of interest to provide
the trade-off of L/D required as a function
of initial glide speed for a given lateral
maneuver capability.
For the case of Global
Coverage, circular initial glide speed re­
quires L/D > 3.56.
For entry at parabolic
speed, V = /Z V G f Global Coverage is avail­
able for any L/D > 2.34.
The general expres­
sion for latitude capability of a Q = 1 aeroglide from initial speed to negligible final
speed is 8
(9)
The parameter Q is a constant in any given
entry.
The minor circle trajectory is
characterized by this parameter Q, which
is just the ratio of lateral force L sin 3
to the r.adial component of centrifugal
force,mV 2 .
A zero value of Q (unbanked
r
vehicle) leads to a maneuver in the orig­
inal orbit plane which is thus a maj or
circle.
Increased values of Q provides
lateral maneuvering.
Only a value of
Q = 1 permits a crossing of the pole from
an entry originally in the equational
plane.
For values of Q greater than unity,
the minor circle is totally on the original
side of the pole.
The bank schedule is sketched in figure
one as a function of speed and the con­
stant parameter Q.
Note that inverted
flight is required at super circular speed.
At circular speed, all values of the Q
parameter indicate 90° bank (wings verti­
cal).
The wings become more level as the
speed decreases in the glide.
2sin<f>T
max
- cos/l_
log
where n is the square of the initial speed
ratio. Global Coverage requires <f> max = 90°,
and the requisite Lift Drag values are shown
in figure three.
The dotted line indicates
the values required for a maximum lateral
range of <(>____ = 45°.
Global Coverage requires a latitude capa­
bility of <f> = 90°, and thus a value of the
minor circle parameter Q of unity.
The
vehicle initially entering in the plane of
the equator can then aeroglide to either
pole .
630
Optimum Turns
Re ferences
Several investigators have searched for
optimum bank control schedules.
From a
distillation of Dynasoar computer runs,
Wallace and Gray 10 present a bank schedule
decreasing with the speed, as in the minor
circle case.
Even their numerical value of
L/D = 3.6 required for Global Coverage is
in excellent agreement with the 3.56 value
found here with the Q = 1 minor circle
glide. Wagner 11 has presented optimized
stepwise bank programs for maximum lateral
range which call out steep bank early in
the glide, followed by reduced bank at the
slower speeds.
General agreement with the
minor circle schedule is observed.
Bryson 12 gave one numerical result of glide
from a subcircular speed which is in general
agreement with minor circle requirements.
D'Elia, G.A., "The Minor Circle Maneu­
ver with Propulsion" (in Italian)
Missili , Fasc. 4, July 1964
Cuadra, Elizabeth and Arthur, Paul D.,
"Orbit Plane Change by External Burning
Aerocruise", AIAA Paper 65-21, January
1965.
To be published, Journal Space­
craft and Rockets.
Drummond, A. M., "Operating Boundaries
for Steady Hypersonic Flight on a Minor
Circle", Journal of the Canadian Aero­
nautics and Space Institute, January
1965, page 1
Fey, Wayne A. "Use of A Lifting Upper
Stage to Achieve Large Offsets During
Ascent to Orbit", AIAA paper 66-60,
January 1966.
Since Q = 1 is the only minor circle turn
to develop ninety degrees lateral range,
early interest was focused on this value.
It has been shown that the maximum lati­
tude is developed along a Q = 1 minor
circle for any L/D value if the maneuver
entry speed is circular.
Slye , R.E., "An analytical method for
studying the lateral motion of atmo­
spheric entry vehicles", NASA TN D-325
(September 1960)
Jackson, W. S., "Special solutions to
the equations of motion for maneuver­
ing entry", Journal of the Aerospace
Sciences, 29,236 (1962)
For a given value of L/D, increasing the
entry speed will increase the minor circle
latitude reached until the limiting value
of 4> max = ARC Sin 2Q
, Further increase in
1+Q 2
initial speed results in lesser latitude,
as the vehicle goes "over the top" for this
given Q.
Moving the value of Q toward unity
permits utilization of additional entry
speed (kinetic energy), with the terminal
case of Q = 1 being reached for any L/D
given high enough entry speed.
At subcir­
cular entry speeds, Q > 1 maneuvers are best:
about Q = 1.25 for the example of reference
12.
At super circular speeds, optimum Q is
usually one .
For aeroglide from circular speed, the max­
imum latitude reached along the Q = 1 ma­
neuver is shown in figure four, using equa­
tion 12.
This curve is also in good agree­
ment with available numerical optimum tra­
jectories 10 and results of complex opti­
mizations 1 -1 .
Arthur, P.D. and Baxter, B.E., "Correc­
tion to Special solutions to the equa­
tions of motion for maneuvering entry,"
AIAA Journal, Vol. 1, No. 10, October
1963, p. 2413.
Arthur, P.D. and Baxter, B.E., "Obser­
vations on Minor Circle Turns", AIAA
Journal, Vol. 1, No. 10, October 1963,
p. 2408.
Arthur, Paul D., "Lateral Maneuvering
in Atmospheric Entry - A comparison of
Cylindrical and Spherical Planet Equa­
tions", Report Number 108, Institute of
Aeronautics, University of Naples,
December 1963
10.
Wallace, R.A., and Gray, W.A., "Minimum
Lift-Drag Ratio Required for Global
Landing Coverage", AIAA Journal , Vol. 1,
No. 11, November 1963, p. 2635
11.
Wagner, W.E., "Roll Modulation for Max­
imum Re-Entry Lateral Range", Journal
Spacecraft and Rockets, Vol. 2 , No. 5 ,
September 1965, p. 677.
12.
Bryson, A.E., Mikami , K., Battle, C.T.,
"Optimum Lateral Turns for a Reentry
Glider" Aerospace Engineering, March
1962, p. 18
Conclusion
Global Coverage in aeroglide atmospheric
entry has been shown feasible for reason­
able values of the vehicle Lift Drag ratio.
The analytically simple minor circle solu­
tion provides a convenient bank schedule
for further study; it also appears that
this bank schedule provides near maximum
lateral capability.
631
——.CYLINDRICAL SOLUTION
——'SPHERICAL SOLUTION
90;
3.56L
(3.56)K
60
-'
QH/2
;30
L/D VALUES ARE FOR GLIDE
FROM CIRCULAR VELOCITY
TO ZERO FINAL VELOCITY
01
CD
CO
CO
301
Fig. 2
60|
JOJ __ _ jl20J
I^JGITUDE !>, (DEGREES)]"
1150.1
Minor Circle Aeroglide Trajectories for Spherical and Cylindrical
Planet Models. Q = 1
90°
60°
D
30'
OL
Fig. 3
l.o
1.2.
1.4
Required Lift Drag Ratio for Global Coverage as a Function of Speed.
A6
Q = 1
Fig. 4
Maximum Latitude Available as a Function of Lift Drag Ratio for Aeroglide
from Circular Speed.
Q = 1